18.1 Different Types of Dividend

The term dividend usually refers to a cash distribution of earnings. If a distribution is made from sources other than current or accumulated retained earnings, the term distribution rather than dividend is used. However, it is acceptable to refer to a distribution from earnings as a dividend and a distribution from capital as a liquidating dividend. More generally, any direct payment by the corporation to shareholders may be considered part of dividend policy.
The most common type of dividend is in the form of cash. Public companies usually pay regular cash dividends twice or four times a year. Sometimes firms will pay a regular cash dividend and an extra cash dividend. Paying a cash dividend reduces corporate cash and retained earnings - except in the case of a liquidating dividend (where paid-in capital may be reduced).
Another type of dividend is paid out in shares of equity. This dividend is referred to as a stock dividend. It is not a true dividend, because no cash leaves the firm. Rather, a stock dividend increases the number of shares outstanding, thereby reducing the value of each share. A stock dividend is commonly expressed as a ratio: for example, with a 2 per cent stock dividend a shareholder receives 1 new share for every 50 currently owned.
When a firm declares a stock split, it increases the number of shares outstanding. Because each share is now entitled to a smaller percentage of the firm’s cash flow, the share price should fall. For example, if the managers of a firm whose equity is selling at 90 rand declare a 3:1 stock split, the price of a share of equity should fall to about 30 rand. A stock split strongly resembles a stock dividend except that it is usually much larger.

18.2 Standard Method of Cash Dividend Payment

p. 489The decision to pay a dividend rests in the hands of the board of directors of the corporation. A dividend is distributable to shareholders of record on a specific date. When a dividend has been declared, it becomes a liability of the firm and cannot be easily rescinded by the corporation. The amount of dividend is expressed as pounds/euros/currency per share (dividend per share), as a percentage of the market price (dividend yield), or as a percentage of earnings per share (dividend payout).
The mechanics of a dividend payment can be illustrated by the example in Fig. 18.1 and the following chronology:

Figure 18.1 Example of procedure for dividend payment

1. Declaration date: On 15 January (the declaration date) the board of directors passes a resolution to pay a dividend of £1 per share on 16 February to all holders of record on 30 January.
2. Date of record: The corporation prepares a list on 30 January of all individuals believed to be shareholders as of this date. The word believed is important here: the dividend will not be paid to individuals whose notification of purchase is received by the company after 30 January.
3. Ex-dividend date: The procedure for the date of record would be unfair if efficient brokerage houses could notify the corporation by 30 January of a trade occurring on 29 January, whereas the same trade might not reach the corporation until 2 February if executed by a less efficient house. To eliminate this problem, all brokerage firms entitle shareholders to receive the dividend if they purchased the equity three business days before the date of record. The second day before the date of record, which is Wednesday 28 January in our example, is called the ex-dividend date. Before this date the shares are said to trade cum dividend.
4. Date of payment: The dividend cheques are mailed to the shareholders on 16 February.

Obviously, the ex-dividend date is important, because an individual purchasing the security before the ex-dividend date will receive the current dividend, whereas another individual purchasing the security on or after this date will not receive the dividend. The share price will therefore fall on the ex-dividend date (assuming no other events occur). It is worth while to note that this drop is an indication of efficiency, not inefficiency, because the market rationally attaches value to a cash dividend. In a world with neither taxes nor transaction costs, the share price would be expected to fall by the amount of the dividend:


p. 490This is illustrated in Fig. 18.2.

Figure 18.2 Price behaviour around the ex-dividend date for a £1 cash dividend

The amount of the price drop may depend on tax rates. For example, consider the case with no capital gains taxes. On the day before an equity goes ex-dividend, a purchaser must decide either (a) to buy the shares immediately and pay tax on the forthcoming dividend, or (b) to buy the shares tomorrow, thereby missing the dividend. If all investors are in the 25 per cent bracket and the dividend is £1, the share price should fall by £0.75 on the ex-dividend date. That is, if the share price falls by this amount on the ex-dividend date, purchasers will receive the same return from either strategy.
As an example of the price drop on the ex-dividend date, consider an extraordinary dividend paid by Microsoft in 2004. The shares went ex dividend on 15 November 2004 with a total dividend of $3.08 per share, consisting of a $3 special dividend and a $0.08 regular dividend. The following share price chart shows the price of Microsoft shares on each of the four days prior to the ex-dividend date and on the ex-dividend date:

The shares closed at $29.97 on 12 November (a Friday) and opened at $27.34 on 15 November, a drop of $2.63. With a 15 per cent tax rate on dividends we would have expected a drop of $2.62, and the actual price drop was almost exactly that amount.

p. 491A powerful argument can be made that dividend policy does not matter. This will be illustrated with the Bristol Corporation. Bristol is an all-equity firm started 10 years ago. The current financial managers know at the present time (date 0) that the firm will dissolve in one year (date 1). At date 0 the managers are able to forecast cash flows with perfect certainty. The managers know that the firm will receive a cash flow of £10,000 immediately and another £10,000 next year. Bristol has no additional positive NPV projects.

Current Policy: Dividends Set Equal to Cash Flow

At the present time, dividends (Div) at each date are set equal to the cash flow of £10,000. The value of the firm can be calculated by discounting these dividends. This value is expressed as

where Div₀ and Div₁ are the cash flows paid out in dividends, and R_S is the discount rate. The first dividend is not discounted because it will be paid immediately.
Assuming R_S = 10 per cent, the value of the firm is

If 1,000 shares are outstanding, the value of each share is

To simplify the example, we assume that the ex-dividend date is the same as the date of payment. After the imminent dividend is paid, the share price will immediately fall to £9.09 (= £19.09 - £10). Several members of Bristol’s board have expressed dissatisfaction with the current dividend policy and have asked you to analyse an alternative policy.

Alternative Policy: Initial Dividend Is Greater than Cash Flow

Another policy is for the firm to pay a dividend of £11 per share immediately, which is, of course, a total dividend payout of £11,000. Because the cash runoff is only £10,000, the extra £1,000 must be raised in one of a few ways. Perhaps the simplest would be to issue £1,000 of bonds or equity now (at date 0). Assume that equity is issued, and the new shareholders will desire enough cash flow at date 1 to let them earn the required 10 per cent return on their date 0 investment. The new shareholders will demand £1,100 of the date 1 cash flow, leaving only £8,900 to the old shareholders. The dividends to the old shareholders will be these:

The present value of the dividends per share is therefore

Students often find it instructive to determine the price at which the new equity is issued. Because the new shareholders are not entitled to the immediate dividend, they would pay £8.09 (= £8.90/1.1) per share. Thus 123.61 (= £1,000/£8.09) new shares are issued.

The Indifference Proposition

p. 492Note that the values in Eqs (18.1) and (18.2) are equal. This leads to the initially surprising conclusion that the change in dividend policy did not affect the value of a share of equity. However, on reflection, the result seems sensible. The new shareholders are parting with their money at date 0 and receiving it back with the appropriate return at date 1. In other words, they are taking on a zero NPV investment. As illustrated in Fig. 18.3, old shareholders are receiving additional funds at date 0 but must pay the new shareholders their money with the appropriate return at date 1. Because the old shareholders must pay back principal plus the appropriate return, the act of issuing new equity at date 0 will not increase or decrease the value of the old shareholders’ holdings. That is, they are giving up a zero NPV investment to the new shareholders. An increase in dividends at date 0 leads to the necessary reduction of dividends at date 1, so the value of the old shareholders’ holdings remains unchanged.

Figure 18.3 Current and alternative dividend policies

This illustration is based on the pioneering work of Miller and Modigliani (MM). Although our presentation is in the form of a numerical example, the MM paper proves that investors are indifferent to dividend policy in a more general setting.

Homemade Dividends

To illustrate the indifference investors have towards dividend policy in our example, we used present value equations. An alternative and perhaps more intuitively appealing explanation avoids the mathematics of discounted cash flows.
p. 493Suppose individual investor X prefers dividends per share of £10 at both dates 0 and 1. Would she be disappointed when informed that the firm’s management is adopting the alternative dividend policy (dividends of £11 and £8.90 on the two dates, respectively)? Not necessarily: she could easily reinvest the £1 of unneeded funds received on date 0, yielding an incremental return of £1.10 at date 1. Thus she would receive her desired net cash flow of £11 - £1 = £10 at date 0 and £8.90 + £1.10 = £10 at date 1.
Conversely, imagine investor Z preferring £11 of cash flow at date 0 and £8.90 of cash flow at date 1, who finds that management will pay dividends of £10 at both dates 0 and 1. He can sell off shares of equity at date 0 to receive the desired amount of cash flow. That is, if he sells off shares (or fractions of shares) at date 0 totalling £1, his cash flow at date 0 becomes £10 + £1 = £11. Because a £1 sale of shares at date 0 will reduce his dividends by £1.10 at date 1, his net cash flow at date 1 would be £10 - £1.10 = £8.90.
The example illustrates how investors can make homemade dividends. In this instance, corporate dividend policy is being undone by a potentially dissatisfied shareholder. This homemade dividend is illustrated by Fig. 18.4. Here the firm’s cash flows of £10 per share at both dates 0 and 1 are represented by point A. This point also represents the initial dividend payout. However, as we just saw, the firm could alternatively pay out £11 per share at date 0 and £8.90 per share at date 1, a strategy represented by point B. Similarly, by either issuing new equity or buying back old equity, the firm could achieve a dividend payout represented by any point on the diagonal line.

Figure 18.4 Homemade dividends: a trade-off between dividends per share at date 0 and dividends per share at date 1

The previous paragraph describes the choices available to the managers of the firm. The same diagonal line also represents the choices available to the shareholder. For example, if the shareholder receives a per-share dividend distribution of (£11, £8.90), he or she can either reinvest some of the dividends to move down and to the right on the graph, or sell off shares of equity and move up and to the left.
The implications of the graph can be summarized in two sentences:

1. By varying dividend policy, managers can achieve any payout along the diagonal line in Fig. 18.4.
2. Either by reinvesting excess dividends at date 0 or by selling off shares of equity at this date, an individual investor can achieve any net cash payout along the diagonal line.

Thus because both the corporation and the individual investor can move only along the diagonal line, dividend policy in this model is irrelevant. The changes the managers make in dividend policy can be undone by an individual who, by either reinvesting dividends or selling off equity, can move to a desired point on the diagonal line.
p. 494

A Test

You can test your knowledge of this material by examining these true statements:

1. Dividends are relevant.
2. Dividend policy is irrelevant.

The first statement follows from common sense. Clearly, investors prefer higher dividends to lower dividends at any single date if the dividend level is held constant at every other date. In other words, if the dividend per share at a given date is raised while the dividend per share for each other date is held constant, the share price will rise. This act can be accomplished by management decisions that improve productivity, increase tax savings, or strengthen product marketing. In fact, you may recall that in Chapter 5 we argued that the value of a firm’s equity is equal to the discounted present value of all its future dividends.
The second statement is understandable once we realize that dividend policy cannot raise the dividend per share at one date while holding the dividend level per share constant at all other dates. Rather, dividend policy merely establishes the trade-off between dividends at one date and dividends at another date. As we saw in Fig. 18.4, an increase in date 0 dividends can be accomplished only by a decrease in date 1 dividends. The extent of the decrease is such that the present value of all dividends is not affected.
Thus, in this simple world, dividend policy does not matter. That is, managers choosing either to raise or to lower the current dividend do not affect the current value of their firm. This theory is powerful, and the work of MM is generally considered a classic in modern finance. With relatively few assumptions, a rather surprising result is shown to be perfectly true. Nevertheless, because we want to examine many real-world factors ignored by MM, their work is only a starting point in this chapter’s discussion of dividends. Later parts of this chapter investigate these real-world considerations.

Dividends and Investment Policy

The preceding argument shows that an increase in dividends through issuance of new shares neither helps nor hurts the shareholders. Similarly, a reduction in dividends through share repurchases neither helps nor hurts shareholders.
What about reducing capital expenditures to increase dividends? Earlier chapters show that a firm should accept all positive net present value projects. To do otherwise would reduce the value of the firm. Thus we have an important point:
Firms should never give up a positive NPV project to increase a dividend (or to pay a dividend for the first time).
This idea was implicitly considered by Miller and Modigliani. One of the assumptions under-lying their dividend irrelevance proposition was this: ‘The investment policy of the firm is set ahead of time and is not altered by changes in dividend policy.’
As later sections will show, there is always more to real life than theory predicts.

18.4 Share Repurchases

p. 495Instead of paying dividends, a firm may use cash to repurchase shares of its own equity. Share repurchases have taken on increased importance in recent years. Consider Fig. 18.5, which shows the average ratios of dividends to earnings, repurchases to earnings, and total payout (both dividends and repurchases) to earnings for US industrial firms over the years from 1984 to 2004. As can be seen, the ratio of repurchases to earnings was far less than the ratio of dividends to earnings in the early years. However, the ratio of repurchases to earnings exceeded the ratio of dividends to earnings by 1998. This trend reversed after 1999, with the ratio of repurchases to earnings falling slightly below the ratio of dividends to earnings by 2004.

Figure 18.5 Ratios of various payouts to earnings

Across Europe the pattern is historically quite different, most notably because share re-purchases were not common, and in several cases were illegal, on the continent and the UK. For example, Ferris, Sen and Yui¹ show that, in 2002, less than 1 per cent of all British firms repurchased shares. Similarly, Rau and Vermaelen² report that although the level of British repurchases is low, the activity was significantly more common in the UK than in the rest of Europe combined. However, in recent years the pattern has shifted significantly, and by 2005 share repurchases were over half the value of all cash dividends in the European Union.³ Table 18.1 shows the trend in share repurchases over the period 1989 to 2005. It is clear that, in all countries, share repurchases have become a much more important part of payout policy since 1999.

Table 18.1 Share repurchases in Europe between 1989 and 2005

Share repurchases are typically accomplished in one of three ways. First, companies may simply purchase their own equity, just as anyone would buy shares of a particular company. In these open market purchases the firm does not reveal itself as the buyer. Thus the seller does not know whether the shares were sold back to the firm or to just another investor.
Second, the firm could institute a tender offer. Here, the firm announces to all of its shareholders that it is willing to buy a fixed number of shares at a specific price. For example, suppose Arts and Crafts (A&C) NV has 1 million shares outstanding, with a share price of €50. The firm makes a tender offer to buy back 300,000 shares at €60 per share. A&C chooses a price above €50 to induce shareholders to sell - that is, tender - their shares. In fact, if the tender price is set high enough, shareholders may want to sell more than the 300,000 shares. In the extreme case where all outstanding shares are tendered, A&C will buy back 3 out of every 10 shares that a shareholder has.
p. 496Finally, firms may repurchase shares from specific individual shareholders, a procedure called a targeted repurchase. For example, suppose International Biotechnology AB purchased approximately 10 per cent of the outstanding shares of Prime Robotics Ltd (P-R Ltd) in April at around SKr38 per share. At that time, International Biotechnology announced to the Stockholm Stock Exchange that it might eventually try to take control of P-R Ltd. In May, P-R Ltd repurchased International Biotechnology holdings at SKr48 per share, well above the market price at that time. This offer was not extended to other shareholders.
p. 497Companies engage in targeted repurchases for a variety of reasons. In some rare cases a single large shareholder can be bought out at a price lower than that in a tender offer. The legal fees in a targeted repurchase may also be lower than those in a more typical buyback. In addition, the shares of large shareholders are often repurchased to avoid a takeover unfavourable to management.
We now consider an example of a repurchase presented in the theoretical world of a perfect capital market. We next discuss real-world factors involved in the repurchase decision.

Dividend versus Repurchase: Conceptual Example

Imagine that Telephonic Industries has excess cash of £300,000 (or £3 per share) and is considering an immediate payment of this amount as an extra dividend. The firm forecasts that, after the dividend, earnings will be £450,000 per year, or £4.50 for each of the 100,000 shares outstanding. Because the price–earnings ratio is 6 for comparable companies, the shares of the firm should sell for £27 (= £4.50 × 6) after the dividend is paid. These figures are presented in the top half of Table 18.2. Because the dividend is £3 per share, the equity would have sold for £30 a share before payment of the dividend.
Alternatively, the firm could use the excess cash to repurchase some of its own equity. Imagine that a tender offer of £30 a share is made. Here, 10,000 shares are repurchased so that the total number of shares remaining is 90,000. With fewer shares outstanding, the earnings per share will rise to £5 (= £450,000/90,000). The price–earnings ratio remains at 6 because both the business and financial risks of the firm are the same in the repurchase case as they were in the dividend case. Thus the price of a share after the repurchase is £30 (= £5 × 6). These results are presented in the bottom half of Table 18.2.
If commissions, taxes and other imperfections are ignored in our example, the shareholders are indifferent between a dividend and a repurchase. With dividends each shareholder owns a share worth £27 and receives £3 in dividends, so that the total value is £30. This figure is the same as both the amount received by the selling shareholders and the value of the equity for the remaining shareholders in the repurchase case.
This example illustrates the important point that, in a perfect market, the firm is indifferent between a dividend payment and a share repurchase. This result is quite similar to the indifference propositions established by MM for debt versus equity financing and for dividends versus capital gains.

Table 18.2 Dividend versus repurchase example for telephonic Industries

p. 498You may often read in the popular financial press that a repurchase agreement is beneficial because earnings per share increase. Earnings per share do rise for Telephonic Industries if a repurchase is substituted for a cash dividend: the EPS is £4.50 after a dividend and £5 after the repurchase. This result holds because the drop in shares after a repurchase implies a reduction in the denominator of the EPS ratio.
However, the financial press frequently places undue emphasis on EPS figures in a repurchase agreement. Given the irrelevance propositions we have discussed, the increase in EPS here is not beneficial. Table 18.2 shows that, in a perfect capital market, the total value to the shareholder is the same under the dividend payment strategy as under the repurchase strategy.

Dividends versus Repurchases: Real-World Considerations

We previously referred to Fig. 18.5, which showed growth in share repurchases relative to dividends. Why do some firms choose repurchases over dividends? Here are perhaps five of the most common reasons.
1. Flexibility Firms often view dividends as a commitment to their shareholders, and are quite hesitant to reduce an existing dividend. Repurchases do not represent a similar commitment. Thus a firm with a permanent increase in cash flow is likely to increase its dividend. Conversely, a firm whose cash flow increase is only temporary is likely to repurchase shares of equity.
2. Executive Compensation Executives are frequently given share options as part of their overall compensation. Let’s revisit the Telephonic Industries example of Table 18.2, where the firm’s equity was selling at £30 when the firm was considering either a dividend or a repurchase. Further imagine that Telephonic had granted 1,000 share options to its CEO, Ralph Taylor, two years earlier. At that time the share price was, say, only £20. This means that Mr Taylor can buy 1,000 shares for £20 a share at any time between the grant of the options and their expiration, a procedure called exercising the options. His gain from exercising is directly proportional to the rise in the share price above £20. As we saw in the example, the price of the equity would fall to £27 following a dividend, but would remain at £30 following a repurchase. The CEO would clearly prefer a repurchase to a dividend, because the difference between the share price and the exercise price of £20 would be £10 (= £30 - £20) following the repurchase but only £7 (= £27 - £20) following the dividend. Existing share options will always have greater value when the firm repurchases shares instead of paying a dividend, because the share price will be greater after a repurchase than after a dividend.
3. Offset to Dilution In addition, the exercise of share options increases the number of shares outstanding. In other words, exercise causes dilution of the shares. Firms frequently buy back shares of equity to offset this dilution. However, it is hard to argue that this is a valid reason for repurchase. As we showed in Table 18.2, repurchase is neither better nor worse for the shareholders than a dividend. Our argument holds whether or not share options have been exercised previously.
4. Undervaluation Many companies buy back shares because they believe that a repurchase is their best investment. This occurs more frequently when managers believe that the share price is temporarily depressed.
The fact that some companies repurchase their equity when they believe it is undervalued does not imply that the management of the company must be correct; only empirical studies can make this determination. The immediate market reaction to the announcement of a share repurchase is usually quite favourable. In addition, some empirical work has shown that the long-term share price performance of securities after a buyback is better than the share price performance of comparable companies that do not repurchase.
5. Taxes Because taxes for both dividends and share repurchases are treated in depth in the next section, suffice it to say at this point that repurchases provide a tax advantage over dividends.

18.5 Personal Taxes and Dividends

p. 499Section 18.3 asserted that in a world without taxes and other frictions, dividend policy is irrelevant. Similarly, Section 18.4 concluded that the choice between a share repurchase and a dividend is irrelevant in a world of this type. This section examines the effect of taxes on both dividends and repurchases. Our discussion is facilitated by classifying firms into two types: those without sufficient cash to pay a dividend, and those with sufficient cash to do so.

Firms without Sufficient Cash to Pay a Dividend

It is simplest to begin with a firm without cash and owned by a single entrepreneur. If this firm should decide to pay a dividend of £100, it must raise capital. The firm might choose among a number of different equity and bond issues to pay the dividend. However, for simplicity, we assume that the entrepreneur contributes cash to the firm by issuing shares to himself. This transaction, diagrammed in the left side of Fig. 18.6, would clearly be a wash in a world of no taxes. £100 cash goes into the firm when equity is issued, and is immediately paid out as a dividend. Thus the entrepreneur neither benefits nor loses when the dividend is paid, a result consistent with Miller-Modigliani.

Figure 18.6 Firm issues equity to pay a dividend

Now assume that dividends are taxed at the owner’s personal tax rate of 25 per cent (in the UK, this is the effective tax rate on dividend income for individuals earning over £34,800⁴). The firm still receives £100 upon issuance of equity. However, the entrepreneur does not get to keep the full £100 dividend. Instead the dividend payment is taxed, implying that the owner receives only £75 net after tax. Thus the entrepreneur loses £25.
Though the example is clearly contrived and unrealistic, similar results can be reached for more plausible situations. Thus financial economists generally agree that, in a world of personal taxes, firms should not issue equity to pay dividends.
The direct costs of issuance will add to this effect. Bankers must be paid when new capital is raised. Thus the net receipts due to the firm from a new issue are less than 100 per cent of total capital raised. Because the size of new issues can be lowered by a reduction in dividends, we have another argument in favour of a low-dividend policy.
Of course, our advice not to finance dividends through new equity issues might need to be modified somewhat in the real world. A company with a large and steady cash flow for many years in the past might be paying a regular dividend. If the cash flow unexpectedly dried up for a single year, should new equity be issued so that dividends could be continued? Although our previous discussion would imply that new equity should not be issued, many managers might issue the equity anyway, for practical reasons. In particular, shareholders appear to prefer dividend stability. Thus managers might be forced to issue equity to achieve this stability, knowing full well the adverse tax consequences.
p. 500

Firms with Sufficient Cash to Pay a Dividend

The previous discussion argued that in a world with personal taxes, a firm should not issue equity to pay a dividend. Does the tax disadvantage of dividends imply the stronger policy, ‘Never, under any circumstances, pay dividends in a world with personal taxes’?
We argue next that this prescription does not necessarily apply to firms with excess cash. To see this, imagine a firm with £1 million in extra cash after selecting all positive NPV projects and determining the level of prudent cash balances. The firm might consider the following alternatives to a dividend:

1. Select additional capital budgeting projects. Because the firm has taken all the available positive NPV projects already, it must invest its excess cash in negative NPV projects. This is clearly a policy at variance with the principles of corporate finance.
   In spite of our distaste for this policy, researchers have suggested that many managers purposely take on negative NPV projects in lieu of paying dividends.⁵ The idea here is that managers would rather keep the funds in the firm because their prestige, pay and perquisites are often tied to the firm’s size. Although managers may help themselves here, they are hurting shareholders. We broached this subject in the section titled ‘Free Cash Flow’ in Chapter 16, and we shall have more to say about it later in this chapter.
2. Acquire other companies. To avoid the payment of dividends, a firm might use excess cash to acquire another company. This strategy has the advantage of acquiring profitable assets. However, a firm often incurs heavy costs when it embarks upon an acquisition programme. In addition, acquisitions are invariably made above the market price. Premiums of 20 to 80 per cent are not uncommon. Because of this, a number of researchers have argued that mergers are not generally profitable to the acquiring company, even when firms are merged for a valid business purpose. Therefore a company making an acquisition merely to avoid a dividend is unlikely to succeed.
3. Purchase financial assets. The strategy of purchasing financial assets in lieu of a dividend payment can be illustrated with the following example.
   

   EXAMPLE 18.1 Dividends and Taxes The Dutch firm Regional Electric NV has €1,000 of extra cash. It can retain the cash and invest it in Treasury bills yielding 10 per cent, or it can pay the cash to shareholders as a dividend. Shareholders can also invest in Treasury bills with the same yield. In the Netherlands the effective corporate tax rate is 30 per cent and the dividend tax rate is 15 per cent. The personal tax rate is an incremental system whereby different tax rates are levied on different salary bands. This means that each individual will have a unique personal tax rate, dependent on their individual salary. Assume, for simplicity, that the effective personal tax rate for shareholders is 28 per cent. How much cash will investors have after five years under each policy?

   
   If dividends are paid now, shareholders will receive
   
   today after taxes. Because their return after personal tax on Treasury bills is 7.2 [= 10 × (1 − 0.28)] per cent, shareholders will have
   
   in five years. Note that interest income is taxed at the personal tax rate (28 per cent in this example), but dividends are taxed at the lower rate of 15 per cent.
   p. 501If Regional Electric NV retains the cash to invest in Treasury bills, its after-tax interest rate will be 0.07 [= 0.10 × (1 − 0.3)]. At the end of five years, the firm will have
   
   If these proceeds are then paid as a dividend, the shareholders will receive
   
   after personal taxes at date 5. The value in Eq. (18.3) is greater than that in Eq. (18.4), implying that cash to shareholders will be greater if the firm pays the dividend now.
   This example shows that for a firm with extra cash the dividend payout decision will depend on personal and corporate tax rates. If personal tax rates are higher than corporate tax rates, a firm will have an incentive to reduce dividend payouts. However, if personal tax rates are lower than corporate tax rates, a firm will have an incentive to pay out any excess cash as dividends.
   Table 16.2 shows quite clearly that tax systems differ considerably across countries. In some countries many investors face marginal tax rates that are above the corporate tax rate. However, at the same time, many investors face marginal tax rates well below the maximum. The interaction between personal and corporate tax rates within a country will mean that the environment faced by investors will be unique and a function of where they stay. As a result, firms may or may not have an incentive not to hoard cash. This is an important point, because many US textbooks (which consider only the US environment) would argue that firms will pay dividends because of tax reasons. However, from a European or Asian perspective, this may not necessarily be a valid assertion.
4. Repurchase shares. The example we described in the previous section showed that investors are indifferent between share repurchase and dividends in a world without taxes and transaction costs. However, under current international tax laws, shareholders will generally prefer a repurchase to a dividend.
   As an example, consider an individual receiving a dividend of €1 on each of 100 shares of an equity. With a 15 per cent tax rate, that individual would pay taxes of €15 on the dividend. Selling shareholders would pay lower taxes if the firm repurchased €100 of existing shares. This occurs because taxes are paid only on the profit from a sale. The individual’s gain on a sale would be only €40 if the shares sold for €100 were originally purchased for, say, €60. The capital gains tax would be €6 (= 0.15 × €40), a number below the tax on dividends of €15. Note that the tax from a repurchase is less than the tax on a dividend, even though the same 15 per cent tax rate applies to both the repurchase and the dividend.
   Of all the alternatives to dividends mentioned in this section, the strongest case can be made for repurchases. In fact, academics have long wondered why firms ever pay a dividend instead of repurchasing shares. There have been at least two possible reasons for avoiding repurchases. First, in many countries, including the UK, there is the fear that share repurchase programmes can lead to illegal price manipulation. Second, tax authorities can penalize firms repurchasing their own shares if the only reason is to avoid the taxes that would be levied on dividends. However, this threat has not materialized with the growth in corporate repurchases.

Summary of Personal Taxes

This section suggests that, because of personal taxes, firms have an incentive to reduce dividends. For example, they might increase capital expenditures, acquire other companies, or purchase financial assets. However, because of financial considerations and legal constraints, rational firms with large cash flows will probably exhaust these activities with plenty of cash left over for dividends.
p. 502It is harder to explain why firms pay dividends instead of repurchasing shares. The tax savings from buybacks are significant, and fear of either the stock exchange or tax authorities seems overblown. Academics are of two minds here. Some argue that corporations were simply slow to grasp the benefits from repurchases. However, since the idea has now firmly caught on, the trend towards replacement of dividends with buybacks will continue. We might even conjecture that dividends will be as unimportant in the future as repurchases were in the past. Conversely, others argue that companies have paid dividends all along for good reason. Perhaps the legal hassles, particularly from tax authorities, are significant after all. Or there may be other, more subtle benefits from dividends. We consider potential benefits of dividends in the next section.

18.6 Real-World Factors Favouring a High-Dividend Policy

The previous section pointed out that because individuals pay taxes on dividends, financial managers might seek ways to reduce dividends. While we discussed the problems with taking on more capital budgeting projects, acquiring other firms, and hoarding cash, we stated that a share repurchase has many of the benefits of a dividend, with less of a tax disadvantage. This section considers reasons why a firm might pay its shareholders high dividends even in the presence of personal taxes on these dividends.

Desire for Current Income

It has been argued that many individuals desire current income. The classic example is the group of retired people and others living on a fixed income. The argument further states that these individuals would bid up the share price should dividends rise, and bid down the share price should dividends fall.
This argument does not hold in Miller and Modigliani’s theoretical model. An individual preferring high current cash flow but holding low-dividend securities could easily sell off shares to provide the necessary funds. Thus in a world of no transactions costs a high-current-dividend policy would be of no value to the shareholder.
However, the current income argument is relevant in the real world. Equity sales involve brokerage fees and other transaction costs - direct cash expenses that could be avoided by an investment in high-dividend securities. In addition, equity sales are time-consuming, further leading investors to buy high-dividend securities.
To put this argument in perspective, remember that financial intermediaries such as mutual funds can perform repackaging transactions at low cost. Such intermediaries could buy low-dividend equities and, by a controlled policy of realizing gains, pay their investors at a higher rate.

Behavioural Finance

Suppose it turned out that the transaction costs in selling no-dividend securities could not account for the preference of investors for dividends. Would there still be a reason for high dividends? We introduced the topic of behavioural finance in Chapter 13, pointing out that the ideas of behaviourists represent a strong challenge to the theory of efficient capital markets. It turns out that behavioural finance also has an argument for high dividends.
The basic idea here concerns self-control, a concept that, though quite important in psychology, has received virtually no emphasis in finance. Although we cannot review all that psychology has to say about self-control, let’s focus on one example - losing weight. Suppose Alfred Martin, a university student, just got back from the Christmas break more than a few pounds heavier than he would like. Alfred wishes to lose weight through doing yoga. Each day Alfred would balance the costs and the benefits of doing yoga. Perhaps he would choose to exercise on most days, because losing the weight is important to him. However, when he is too busy with exams, he might rationally choose not to exercise, because he cannot afford the time. So he may rationally choose to avoid doing yoga on days when other social commitments become too time-consuming.
p. 503Unfortunately, Alfred must make a proactive choice to do yoga every day, and there may be too many days when his lack of self-control gets the better of him. He may tell himself that he doesn’t have the time to exercise on a particular day, simply because he is starting to find yoga boring, not because he really doesn’t have the time. Before long, he is avoiding yoga on most days - and overeating in reaction to the guilt from not exercising!
Is there an alternative? One way would be to set rigid rules. Perhaps Alfred may decide to do yoga every day no matter what. This is not necessarily the best approach for everyone, but there is no question that many of us (perhaps most of us) live by a set of rules.
What does this have to do with dividends? Investors must also deal with self-control. Suppose a retiree wants to consume £20,000 a year from savings, in addition to her pension. On the one hand, she could buy shares with a dividend yield high enough to generate £20,000 in dividends. On the other hand, she could place her savings in no-dividend shares, selling off £20,000 each year for consumption. Though these two approaches seem equivalent financially, the second one may allow for too much leeway. If lack of self-control gets the better of her, she might sell off too much, leaving little for her later years. Better, perhaps, to short-circuit this possibility by investing in dividend-paying equities with a firm personal rule of never ‘dipping into principal’. Although behaviourists do not claim that this approach is for everyone, they argue that enough people think this way to explain why firms pay dividends - even though, as we said earlier, dividends are tax-disadvantaged.
Does behavioural finance argue for increased share repurchases as well as increased dividends? The answer is no, because investors will sell the shares that firms repurchase. As we have said, selling shares involves too much leeway. Investors might sell too many shares, leaving little for later years. Thus the behaviourist argument may explain why companies pay dividends in a world with personal taxes.

Agency Costs

Although shareholders, bondholders and management form firms for mutually beneficial reasons, one party may later gain at the other’s expense. For example, take the potential conflict between bondholders and shareholders. Bondholders would like shareholders to leave as much cash as possible in the firm so that this cash would be available to pay the bondholders during times of financial distress. Conversely, shareholders would like to keep this extra cash for themselves. That’s where dividends come in. Managers, acting on behalf of the shareholders, may pay dividends simply to keep the cash away from the bondholders. In other words, a dividend can be viewed as a wealth transfer from bondholders to shareholders. There is empirical evidence for this view of things. For example, DeAngelo and DeAngelo find that firms in financial distress are reluctant to cut dividends.⁶ Of course, bondholders know about the propensity of shareholders to transfer money out of the firm. To protect themselves, bondholders frequently create loan agreements stating that dividends can be paid only if the firm has earnings, cash flow and working capital above specified levels.
Although managers may be looking out for shareholders in any conflict with bondholders, managers may pursue selfish goals at the expense of shareholders in other situations. For example, as discussed in a previous chapter, managers might pad expense accounts, take on pet projects with negative NPVs, or simply not work hard. Managers find it easier to pursue these selfish goals when the firm has plenty of free cash flow. After all, one cannot squander funds if the funds are not available in the first place. And that is where dividends come in. Several scholars have suggested that the board of directors can use dividends to reduce agency costs.⁷ By paying dividends equal to the amount of ‘surplus’ cash flow, a firm can reduce management’s ability to squander the firm’s resources.
This discussion suggests a reason for increased dividends, but the same argument applies to share repurchases as well. Managers, acting on behalf of shareholders, can just as easily keep cash from bondholders through repurchases as through dividends. And the board of directors, also acting on behalf of shareholders, can reduce the cash available to spendthrift managers just as easily through repurchases as through dividends. Thus the presence of agency costs is not an argument for dividends over repurchases. Rather, agency costs imply that firms may increase either dividends or share repurchases rather than hoard large amounts of cash.
p. 504

Information Content of Dividends, and Dividend Signalling

Information Content While there are many things researchers do not know about dividends, we know one thing for sure: the share price of a firm generally rises when the firm announces a dividend increase, and generally falls when a dividend reduction is announced. For example, Asquith and Mullins estimate that share prices rise about 3 per cent following announcements of dividend initiations.⁸ Michaely, Thaler and Womack find that share prices fall about 7 per cent following announcements of dividend omissions.⁹
The question is how we should interpret this empirical evidence. Consider the following three positions on dividends:

1. From the homemade dividend argument of MM, dividend policy is irrelevant, given that future earnings (and cash flows) are held constant.
2. Because of tax effects, a firm’s share price is negatively related to the current dividend when future earnings (or cash flows) are held constant.
3. Because of shareholders’ desire for current income, a firm’s share price is positively related to its current dividend, even when future earnings (or cash flows) are held constant.

At first glance, the empirical evidence that share prices rise when dividend increases are announced may seem consistent with position 3 and inconsistent with positions 1 and 2. In fact, many writers have said this. However, other authors have countered that the observation itself is consistent with all three positions. They point out that companies do not like to cut a dividend. Thus firms will raise the dividend only when future earnings, cash flow and so on are expected to rise enough so that the dividend is not likely to be reduced later to its original level. A dividend increase is management’s signal to the market that the firm is expected to do well.
It is the expectation of good times, and not only the shareholders’ affinity for current income, that raises share price. The rise in the share price following the dividend signal is called the information content effect of the dividend. To recapitulate, imagine that the share price is unaffected or even negatively affected by the level of dividends, given that future earnings (or cash flows) are held constant. Nevertheless, the information content effect implies that share prices may rise when dividends are raised - if dividends simultaneously cause shareholders to increase their expectations of future earnings and cash flows.
Dividend Signalling We just argued that the market infers a rise in earnings and cash flows from a dividend increase, leading to a higher share price. Conversely, the market infers a decrease in cash flows from a dividend reduction, leading to a drop in share price. This raises an interesting corporate strategy: could management increase dividends just to make the market think that cash flows will be higher, even when management knows that cash flows will not rise?
While this strategy may seem dishonest, academics take the position that managers frequently attempt the strategy. Academics begin with the following accounting identity for an all-equity firm:

Equation (18.5) must hold if a firm is neither issuing nor repurchasing equity. That is, the cash flow from the firm must go somewhere. If it is not paid out in dividends, it must be used in some expenditure. Whether the expenditure involves a capital budgeting project or a purchase of Treasury bills, it is still an expenditure.
Imagine that we are in the middle of the year, and investors are trying to make some forecast of cash flow over the entire year. These investors may use Eq. (18.5) to estimate cash flow. For example, suppose the firm announces that current dividends will be £50 million and the market believes that capital expenditures are £80 million. The market would then determine cash flow to be £130 million (= £50 million + £80 million).
Now, suppose that the firm had, alternatively, announced a dividend of £70 million. The market might assume that cash flow remains at £130 million, implying capital expenditures of £60 million (= £130 million - £70 million). Here, the increase in dividends would hurt the share price, because the market anticipates that valuable capital expenditures will be crowded out. Alternatively, the market might assume that capital expenditures remain at £80 million, implying the estimate of cash flow to be £150 million (= £70 million + £80 million). The share price would probably rise here, because share prices usually increase with cash flow. In general, academics believe that models where investors assume capital expenditures remain the same are more realistic. Thus an increase in dividends raises the share price.
p. 505Now we come to the incentives of managers to fool the public. Suppose you are a manager who wants to boost the share price, perhaps because you are planning to sell some of your personal holdings of the company’s equity immediately. You might increase dividends so that the market would raise its estimate of the firm’s cash flow, thereby also boosting the current share price.
If this strategy is appealing, would anything prevent you from raising dividends without limit? The answer is yes, because there is also a cost to raising dividends. That is, the firm will have to forgo some of its profitable projects. Remember that cash flow in Eq. (18.5) is a constant, so an increase in dividends is obtained only by a reduction in capital expenditures. At some point the market will learn that cash flow has not increased, but instead profitable capital expenditures have been cut. Once the market absorbs this information, share prices should fall below what they would have been had dividends never been raised. Thus if you plan to sell, say, half of your shares and retain the other half, an increase in dividends should help you on the immediate sale but hurt you when you sell your remaining shares years later. So your decision on the level of dividends will be based, among other things, on the timing of your personal equity sales.
This is a simplified example of dividend signalling, where the manager sets dividend policy based on maximum benefit for himself.¹¹ Alternatively, a given manager may have no desire to sell his shares immediately but knows that, at any one time, plenty of ordinary shareholders will want to do so. Thus for the benefit of shareholders in general, a manager will always be aware of the trade-off between current and future share price. And this, then, is the essence of signalling with dividends. It is not enough for a manager to set dividend policy to maximize the true (or intrinsic) value of the firm. He must also consider the effect of dividend policy on the current share price, even if the current share price does not reflect true value.
Does a motive to signal imply that managers will increase dividends rather than share repurchases? The answer is probably no: most academic models imply that dividends and share repurchases are perfect substitutes.¹² Rather, these models indicate that managers will consider reducing capital spending (even on projects with positive NPVs) to increase either dividends or share repurchases.

Summary and Conclusions

p. 515

1. The dividend policy of a firm is irrelevant in a perfect capital market, because the shareholder can effectively undo the firm’s dividend strategy. If a shareholder receives a greater dividend than desired, he or she can reinvest the excess. Conversely, if the shareholder receives a smaller dividend than desired, he or she can sell off extra shares of equity. This argument is due to MM, and is similar to their homemade leverage concept, discussed in a previous chapter.
2. Shareholders will be indifferent between dividends and share repurchases in a perfect capital market.
3. Because dividends are taxed, companies should not issue equity to pay out a dividend.
4. Also because of taxes, firms have an incentive to reduce dividends. For example, they might consider increasing capital expenditures, acquiring other companies, or purchasing financial assets. However, because of financial considerations and legal constraints, rational firms with large cash flows will probably exhaust these activities with plenty of cash left over for dividends.
5. In a world with personal taxes, a strong case can be made for repurchasing shares instead of paying dividends.
6. Nevertheless, there are a number of justifications for dividends, even in a world with personal taxes:
   
   1. Investors in no-dividend equities incur transaction costs when selling off shares for current consumption.
   2. Behavioural finance argues that investors with limited self-control can meet current consumption needs via high-dividend equities while adhering to a policy of ‘never dipping into principal’.
   3. Managers, acting on behalf of shareholders, can pay dividends to keep cash from bondholders. The board of directors, also acting on behalf of shareholders, can use dividends to reduce the cash available to spendthrift managers.
7. The stock market reacts positively to increases in dividends (or an initial payment) and negatively to decreases in dividends. This suggests that there is information content in dividend payments.
8. High (low) dividend firms should arise to meet the demands of dividend-preferring (capital-gains-preferring) investors. Because of these clienteles, it is not clear that a firm can create value by changing its dividend policy.
9. Time-varying demand for dividends means that in some periods companies that pay dividends are traded at a premium and in other cases they are not. Managers will time their dividend policies to take advantage of this premium.

chapter 17

17.1 Adjusted Present Value Approach

When financing issues are an important part of an investment proposal, a good methodology to use is the adjusted present value method. The approach separates project cash flows from financing cash flows and values these separately. If the combined present values are positive, the project should be taken. The adjusted present value (APV) method is described by the following formula:
APV = NPV + NPVF
p. 467In words, the value of a project to a levered firm (APV) is equal to the value of the project to an unlevered firm (NPV) plus the net present value of the financing side effects (NPVF). We can generally think of four side effects:

1. The tax subsidy to debt: This was discussed in Chapter 15, where we pointed out that for perpetual debt the value of the tax subsidy is t_CB. (t_C is the corporate tax rate, and B is the value of the debt.) The material about valuation under corporate taxes in Chapter 15 is actually an application of the APV approach.
2. The costs of issuing new securities: As we shall discuss in detail in Chapter 20, bankers participate in the public issuance of corporate debt. These bankers must be compensated for their time and effort, a cost that lowers the value of the project.
3. The costs of financial distress: The possibility of financial distress, and bankruptcy in particular, arises with debt financing. As stated in the previous chapter, financial distress imposes costs, thereby lowering value.
4. Subsidies to debt financing: The interest on debt issued by state and local governments may not be taxable to the investor, or the tax may be discounted. Because of this, the yield on government debt can be substantially below the yield on taxable debt. Frequently corporations can obtain financing from a municipality at the tax-exempt rate because the municipality can borrow at that rate as well. As with any subsidy, this subsidy adds value.

Although each of the preceding four side effects is important, the tax deduction to debt almost certainly has the highest value in most actual situations. For this reason, the following example considers the tax subsidy but not the other three side effects. A later example will deal with all three.
Consider a project of P.B. Singer plc with the following characteristics:

1. Cash inflows: £500,000 per year for the indefinite future.
2. Cash costs: 72 per cent of sales.
3. Initial investment: £520,000.
4. t_C = 28%
5. R₀ = 20 per cent, where R₀ is the cost of capital for a project of an all-equity firm.

If both the project and the firm are financed with only equity, the project’s cash flows are as follows:

The distinction between present value and net present value is important for this example. The present value of a project is determined before the initial investment at date 0 is subtracted. The initial investment is subtracted for the calculation of net present value.
Given a discount rate of 20 per cent, the present value of the project is

The net present value (NPV) of the project - that is, the value of the project to an all-equity firm - is

Because the NPV is negative, the project would be rejected by an all-equity firm.
p. 468Now imagine that the firm finances the project with exactly £135,483.90 in debt, so that the remaining investment of £384,516.10 (= £520,000 - £135,483.90) is financed with equity. The net present value of the project under leverage, which we call the adjusted present value, or the APV, is

That is, the value of the project when financed with some leverage is equal to the value of the project when financed with all equity plus the tax shield from the debt. Because this number is positive, the project should be accepted.
You may be wondering why we chose such a precise amount of debt. Actually, we chose it so that the ratio of debt to the present value of the project under leverage is 0.25.¹
In this example, debt is a fixed proportion of the present value of the project, not a fixed proportion of the initial investment of £520,000. This is consistent with the goal of a target debt-to-market-value ratio, which we find is followed by companies in many countries. For example, banks typically lend to property developers a fixed percentage of the appraised market value of a project, not a fixed percentage of the initial investment.

17.2 Flow to Equity Approach

The flow to equity (FTE) approach is an alternative capital budgeting approach. The formula simply calls for discounting the cash flow from the project to the shareholders of the levered firm at the cost of equity capital, R_S. For a perpetuity this becomes

There are three steps to the FTE approach.

Step 1: Calculating Levered Cash Flow (LCF)²

Assuming an interest rate of 10 per cent, the perpetual cash flow to shareholders in our P.B. Singer plc example is

Alternatively, we can calculate levered cash flow (LCF) directly from unlevered cash flow (UCF). The key here is that the difference between the cash flow that shareholders receive in an unlevered firm and the cash flow that shareholders receive in a levered firm is the after-tax interest payment. (Repayment of principal does not appear in this example because the debt is perpetual.) We write this algebraically as

The term on the right side of this expression is the after-tax interest payment. Thus because cash flow to the unlevered shareholders (UCF) is £100,800 and the after-tax interest payment is £9,754.84 (= 0.72 × 0.10 × £135,483.90), cash flow to the levered shareholders (LCF) is
£100,800 - £9,755 = £91,045
p. 469which is exactly the number we calculated earlier.

Step 2: Calculating 

The next step is to calculate the discount rate, R_S. Note that we assumed that the discount rate on unlevered equity, R₀, is 0.20. As we saw in an earlier chapter, the formula for R_S is

Note that our target debt-to-value ratio of 1/4 implies a target debt-to-equity ratio of 1/3. Applying the preceding formula to this example, we have

Step 3: Valuation

The present value of the project’s LCF is

Because the initial investment is £520,000 and £135,483.90 is borrowed, the firm must advance the project £384,516.10 (= £520,000 - £135,483.90) out of its own cash reserves. The net present value of the project is simply the difference between the present value of the project’s LCF and the investment not borrowed. Thus the NPV is

which is identical to the result found with the APV approach.

17.3 Weighted Average Cost of Capital Method

Finally, we can value a project using the weighted average cost of capital (WACC) method. Although this method was discussed in earlier chapters, it is worth while to review it here. The WACC approach begins with the insight that projects of levered firms are simultaneously financed with both debt and equity. The cost of capital is a weighted average of the cost of debt and cost of equity. The cost of equity is R_S. Ignoring taxes, the cost of debt is simply the borrowing rate, R_B. However, with corporate taxes, the appropriate cost of debt is (1 - t_C)R_B, the after-tax cost of debt.
The formula for determining the weighted average cost of capital, R_WACC, is

The weight for equity, S/(S + B), and the weight for debt, B/(S + B), are target ratios. Target ratios are generally expressed in terms of market values, not accounting values. (Recall that another phrase for accounting value is book value.)
The formula calls for discounting the unlevered cash flow of the project (UCF) at the weighted average cost of capital, R_WACC. The net present value of the project can be written algebraically as

If the project is a perpetuity, the net present value is

p. 470We previously stated that the target debt-to-value ratio of our project is 1/4 and the corporate tax rate is 0.28, implying that the weighted average cost of capital is

Note that R_WACC, 0.186, is lower than the cost of equity capital for an all-equity firm, 0.20. This must always be the case, because debt financing provides a tax subsidy that lowers the average cost of capital.
We previously determined the UCF of the project to be £100,800, implying that the present value of the project is

This initial investment is £520,000, so the NPV of the project is:

Note that all three approaches yield the same value.

17.4 A Comparison of the APV, FTE and WACC Approaches

Capital budgeting techniques in the early chapters of this text applied to all-equity firms. Capital budgeting for the levered firm could not be handled earlier in the book, because the effects of debt on firm value were deferred until the previous two chapters. We learned there that debt increases firm value through tax benefits, but decreases value through bankruptcy and related costs.
In this chapter, we provide three approaches to capital budgeting for the levered firm. The adjusted present value (APV) approach first values the project on an all-equity basis. That is, the project’s after-tax cash flows under all-equity financing (called unlevered cash flows, or UCF) are placed in the numerator of the capital budgeting equation. The discount rate, assuming all-equity financing, appears in the denominator. At this point, the calculation is identical to that performed in the early chapters of this book. We then add the net present value of the debt. We point out that the net present value of the debt is likely to be the sum of four parameters: tax effects, flotation costs, bankruptcy costs, and interest subsidies.
The flow to equity (FTE) approach discounts the after-tax cash flow from a project going to the shareholders of a levered firm (LCF). LCF, which stands for levered cash flow, is the residual to shareholders after interest has been deducted. The discount rate is R_S, the cost of capital to the shareholders of a levered firm. For a firm with leverage, R_S must be greater than R₀, the cost of capital for an unlevered firm. This follows from our material in Chapter 15 showing that leverage raises the risk to the shareholders.
The last approach is the weighted average cost of capital (WACC) method. This technique calculates the project’s after-tax cash flows assuming all-equity financing (UCF). The UCF is placed in the numerator of the capital budgeting equation. The denominator, R_WACC, is a weighted average of the cost of equity capital and the cost of debt capital. The tax advantage of debt is reflected in the denominator, because the cost of debt capital is determined net of corporate tax. The numerator does not reflect debt at all.

Which Method Is Best?

The net present value of our project is exactly the same under each of the three methods. In theory, this should always be the case.³ However, one method usually provides an easier computation than another, and in many cases one or more of the methods are virtually impossible computationally. We first consider when it is best to use the WACC and FTE approaches.
If the risk of a project stays constant throughout its life, it is plausible to assume that R₀ remains constant throughout the project’s life. This assumption of constant risk appears to be reasonable for most real-world projects. In addition, if the debt-to-value ratio remains constant over the life of the project, both R_S and R_WACC will remain constant as well. Under this latter assumption, either the FTE or the WACC approach is easy to apply. However, if the debt-to-value ratio varies from year to year, both R_S and R_WACC vary from year to year as well. Using the FTE or the WACC approach when the denominator changes every year is computationally quite complex, and when computations become complex, the error rate rises. Thus both the FTE and WACC approaches present difficulties when the debt-to-value ratio changes over time.
p. 471The APV approach is based on the level of debt in each future period. Consequently, when the debt level can be specified precisely for future periods, the APV approach is quite easy to use. However, when the debt level is uncertain, the APV approach becomes more problematic. For example, when the debt-to-value ratio is constant, the debt level varies with the value of the project. Because the value of the project in a future year cannot be easily forecast, the level of debt cannot be easily forecast either.
Thus we suggest the following guideline:
Use WACC or FTE if the firm’s target debt-to-value ratio applies to the project over its life. Use APV if the project’s level of debt is known over the life of the project.
There are a number of situations where the APV approach is preferred. For example, in a leveraged buyout (LBO) the firm begins with a large amount of debt but rapidly pays down the debt over a number of years. Because the schedule of debt reduction in the future is known when the LBO is arranged, tax shields in every future year can be easily forecast. Thus the APV approach is easy to use here. (An illustration of the APV approach applied to LBOs is provided in the appendix to this chapter.) By contrast, the WACC and FTE approaches are virtually impossible to apply here, because the debt-to-equity value cannot be expected to be constant over time. In addition, situations involving interest subsidies and flotation costs are much easier to handle with the APV approach. Finally, the APV approach handles the lease-versus-buy decision much more easily than does either the FTE or the WACC approach.
The preceding examples are special cases. Typical capital budgeting situations are more amenable to either the WACC or the FTE approach than to the APV approach. In many countries, financial managers think in terms of target debt-to-value ratios. If a project does better than expected, both its value and its debt capacity are likely to rise. The manager will increase debt correspondingly here. Conversely, the manager would be likely to reduce debt if the value of the project were to decline unexpectedly. Of course, because financing is a time-consuming task, the ratio cannot be adjusted daily or monthly. Rather, the adjustment can be expected to occur over the long run. As mentioned before, the WACC and FTE approaches are more appropriate than the APV approach when a firm focuses on a target debt-to-value ratio.
Because of this, we recommend that the WACC and the FTE approaches, rather than the APV approach, be used in most real-world situations. In addition, frequent discussions with business executives have convinced us that the WACC is by far the most widely used method in the real world. Thus practitioners seem to agree with us that, outside the special situations mentioned, the APV approach is a less important method of capital budgeting.⁴

The Three Methods of Capital Budgeting with Leverage

Adjusted present value (APV) method: where UCFt is the project’s cash flow at date t to the equity-holders of an unlevered firm, and R0 is the cost of capital for project in an unlevered firm. p. 472 Flow to equity (FTE) method: where LCFt is the project’s cash flow at date t to the equity-holders of a levered firm, and RS is the cost of equity capital with leverage. Weighted average cost of capital (WACC) method: where RWACC is the weighted average cost of capital. Notes The middle term in the APV formula implies that the value of a project with leverage is greater than the value of the project without leverage. Because RWACC < R0, the WACC formula implies that the value of a project with leverage is greater than the value of the project without leverage. In the FTE method, cash flow after interest (LCF) is used. Initial investment is reduced by amount borrowed as well. Guidelines Use WACC or FTE if the firm’s target debt-to-value ratio applies to the project over its life. Use APV if the project’s level of debt is known over the life of the project.

17.5 Capital Budgeting when the Discount Rate Must Be Estimated

The previous sections of this chapter introduced APV, FTE and WACC - the three basic approaches to valuing a levered firm. However, one important detail remains. The example in Sections 17.1 to 17.3 assumed a discount rate. We now want to show how this rate is determined for real-world firms with leverage, with an application to the three preceding approaches. The example in this section brings together the work in Chapters 9, 10, 11 and 12 on the discount rate for unlevered firms with that in Chapter 15 on the effect of leverage on the cost of capital.

EXAMPLE 17.1 Cost of Capital World-Wide Enterprises (WWE) is a large conglomerate thinking of entering the widget business, where it plans to finance projects with a debt-to-value ratio of 25 per cent (or, alternatively, a debt-to-equity ratio of 1/3). There is currently one firm in the widget industry, Asian Widgets (AW). This firm is financed with 40 per cent debt and 60 per cent equity. The beta of AW’s equity is 1.5. AW has a borrowing rate of 12 per cent, and WWE expects to borrow for its widget venture at 10 per cent. The corporate tax rate for both firms is 0.40, the market risk premium is 8.5 per cent, and the riskless interest rate is 8 per cent. What is the appropriate discount rate for WWE to use for its widget venture? As shown in Sections 17.1, 17.2 and 17.3, a corporation may use one of three capital budgeting approaches: APV, FTE or WACC. The appropriate discount rates for these three approaches are R0, RS and RWACC, respectively. Because AW is WWE’s only competitor in widgets, we look at AW’s cost of capital to calculate R0, RS and RWACC for WWE’s widget venture. The following four-step procedure will allow us to calculate all three discount rates: p. 473 Determining AW’s cost of equity capital: First, we determine AW’s cost of equity capital using the security market line (SML): AW’s cost of equity capital: where M is the expected return on the market portfolio and RF is the risk-free rate. Determining AW’s hypothetical all-equity cost of capital: We must standardize the preceding number in some way, because AW and WWE’s widget ventures have different target debt-to-value ratios. The easiest approach is to calculate the hypothetical cost of equity capital for AW, assuming all-equity financing. This can be determined from MM’s Proposition II under taxes: AW’s cost of capital if all equity: By solving the equation, we find that R0 = 0.1825. Of course, R0 is less than RS because the cost of equity capital would be less when the firm employs no leverage. At this point, firms in the real world generally make the assumption that the business risk of their venture is about equal to the business risk of the firms already in the business. Applying this assumption to our problem, we assert that the hypothetical discount rate of WWE’s widget venture if all equity financed is also 0.1825.5 This discount rate would be employed if WWE uses the APV approach because the APV approach calls for R0, the project’s cost of capital in a firm with no leverage. Determining RS for WWE’s widget venture: Alternatively, WWE might use the FTE approach, where the discount rate for levered equity is determined like this: Cost of equity capital for WWE’s widget venture: Note that the cost of equity capital for WWE’s widget venture, 0.199, is less than the cost of equity capital for AW, 0.2075. This occurs because AW has a higher debt-to-equity ratio. (As mentioned, both firms are assumed to have the same business risk.) Determining RWACC for WWE’s widget venture: Finally, WWE might use the WACC approach. Here is the appropriate calculation: RWACCfor WWE’s widget venture:

p. 474The preceding example shows how the three discount rates, R₀, R_S and R_WACC, are determined in the real world. These are the appropriate rates for the APV, FTE and WACC approaches, respectively. Note that R_S for Asian Widgets is determined first, because the cost of equity capital can be determined from the beta of the firm’s equity. As discussed in an earlier chapter, beta can easily be estimated for any publicly traded firm such as AW.

17.6 APV Example

As mentioned earlier in this chapter, firms generally set a target debt-to-equity ratio, allowing the use of WACC and FTE for capital budgeting. APV does not work as well here. However, as we also mentioned earlier, APV is the preferred approach when there are side benefits and side costs to debt. Because the analysis can be tricky, we now devote an entire section to an example where, in addition to the tax subsidy to debt, both flotation costs and interest subsidies come into play.

EXAMPLE 17.2 APV Bicksler Enterprises is considering a £10 million project that will last five years. The investment will be depreciated at 25 per cent reducing balance for tax purposes. At the end of the five years, the investment will be sold for its residual book value. The cash revenues less cash expenses per year are £3,500,000. The corporate tax bracket is 28 per cent. The risk-free rate is 10 per cent, and the cost of unlevered equity is 20 per cent. First we shall calculate the depreciation in each year. The cash flow projections each year are below. Because the investment is sold at its residual value, there are no tax implications for the final cash flow of £2,373,047. If, for example, Bicksler sold the investment for £3,000,000 it would be liable to pay tax on the profit of £626,953 (£3,000,000 - £2,373,047): We stated before that the APV of a project is the sum of its all-equity value plus the additional effects of debt. We examine each in turn. All-Equity Value Assuming the project is financed with all equity, we shall discount the revenues and initial outlay cash flows by the cost of unlevered equity. The depreciation tax shield should be discounted at the risk-free rate. The present value of each cash flow is given below: p. 475The net present value is thus -£10,000,000 + £2,736,364 + £2,183,884 + £1,754,164 + £1,416,981 + £1,135,521 + £794,729 = £21,642 This calculation uses the techniques presented in the early chapters of this book. Notice again that the depreciation tax shield is discounted at the riskless rate of 10 per cent. The revenues and expenses are discounted at the higher rate of 20 per cent. An all-equity firm would accept the project, because the NPV is £21,642. However, equity flotation costs and economic volatility (not mentioned yet) would more than likely make the NPV negative. However, debt financing may add enough value to the project to justify acceptance. We consider the effects of debt next. Additional Effects of Debt Bicksler Enterprises can obtain a five-year, non-amortizing loan for £7,500,000 after flotation costs at the risk-free rate of 10 per cent. Flotation costs are fees paid when equity or debt is issued. These fees may go to printers, lawyers, and bankers, among others. Bicksler Enterprises is informed that flotation costs will be 1 per cent of the gross proceeds of its loan. The previous chapter indicates that debt financing alters the NPV of a typical project. We look at the effects of debt next. Flotation Costs Given that flotation costs are 1 per cent of the gross proceeds, we have Thus the gross proceeds are This implies flotation costs of £75,758 (= 1% × £7,575,758). To check the calculation, note that net proceeds are £7,500,000 (= £7,575,758 - £75,758). In other words, Bicksler Enterprises receives only £7,500,000. The flotation costs of £75,758 are received by intermediaries such as bankers. Under International Financial Reporting Standards, flotation costs directly attributable to an investment in a particular asset should be depreciated using the same method as the asset itself. In our case, depreciation would be charged on the flotation costs using 25 per cent reducing balance. The tax shield can then be calculated accordingly. Flotation costs are paid immediately, but are deducted from taxes by amortizing on a 25 per cent reducing-balance basis over the life of the loan. The depreciation schedule on the flotation costs is presented below: p. 476The cash flows from flotation costs are as follows: When we discount at 10 per cent, the net cost of flotation is The net present value of the project after the flotation costs of debt but before the benefits of debt is Tax Subsidy Interest must be paid on the gross proceeds of the loan, even though intermediaries receive the flotation costs. Because the gross proceeds of the loan are £7,575,578, annual interest is £757,576 (= £7,575,758 × 0.10). The interest cost after taxes is £545,455 [= £757,576 × (1 − 0.28)]. Because the loan is non-amortizing, the entire debt of £7,575,758 is repaid at date 5. These terms are indicated here: The relevant cash flows are listed in boldface in the preceding table. They are: (a) loan received, (b) annual interest cost after taxes, and (c) repayment of debt. Note that we include the gross proceeds of the loan as an inflow, because the flotation costs have previously been subtracted. In Chapter 15 we mentioned that the financing decision can be evaluated in terms of net present value. The net present value of the loan is simply the sum of the net present values of each of the three cash flows. This can be represented as follows: The calculations for this example are: The NPV (loan) is positive, reflecting the interest tax shield.6 p. 477The adjusted present value of the project with this financing is Though we previously saw that an all-equity firm would probably not accept the project (once equity flotation costs were taken into account), a firm would accept the project if a £7,500,000 (net) loan could be obtained. Because the loan just discussed was at the market rate of 10 per cent, we have considered only two of the three additional effects of debt (flotation costs and tax subsidy) so far. We now examine another loan, where the third effect arises. Non-Market-Rate Financing A number of companies are fortunate enough to obtain subsidized financing from a governmental authority. Suppose that the project of Bicksler Enterprises is deemed socially beneficial, and the British government grants the firm a £7,500,000 loan at 8 per cent interest. In addition, all flotation costs are absorbed by the state. Clearly, the company will choose this loan over the one we previously calculated. Here are the cash flows from the loan: The relevant cash flows are listed in boldface in the preceding table. Using Eq. (17.1), the NPV (loan) is Why do we discount the cash flows in Eq. (17.1″) at 10 per cent when the firm is borrowing at 8 per cent? We discount at 10 per cent because that is the fair or market-wide rate. That is, 10 per cent is the rate at which the firm could borrow without benefit of subsidization. The net present value of the subsidized loan is larger than the net present value of the earlier loan, because the firm is now borrowing at the below-market rate of 8 per cent. Note that the NPV (loan) calculation in Eq. (17.1″) captures both the tax effect and the non-market-rate effect. The net present value of the project with subsidized debt financing is

The preceding example illustrates the adjusted present value (APV) approach. The approach begins with the present value of a project for the all-equity firm. Next, the effects of debt are added in. The approach has much to recommend it. It is intuitively appealing, because individual components are calculated separately and added together in a simple way. And, if the debt from the project can be specified precisely, the present value of the debt can be calculated precisely.

17.7 Beta and Leverage

p. 478A previous chapter provides the formula for the relationship between the beta of the equity and leverage of the firm in a world without taxes. We reproduce this formula here:
The no-tax case:

As pointed out earlier, this relationship holds under the assumption that the beta of debt is zero.
Because firms must pay corporate taxes in practice, it is worth while to provide the relationship in a world with corporate taxes. It can be shown that the relationship between the beta of the unlevered firm and the beta of the levered equity is the following:⁷
The corporate tax case:

when (a) the corporation is taxed at the rate of t_C and (b) the debt has a zero beta.
Because [1 + (1 - t_C)Debt/Equity] must be more than 1 for a levered firm, it follows that β_{Unlevered firm} < β_Equity. The corporate tax case of Eq. (17.4) is quite similar to the no-tax case of Eq. (17.3), because the beta of levered equity must be greater than the beta of the unlevered firm in either case. The intuition that leverage increases the risk of equity applies in both cases.
However, notice that the two equations are not equal. It can be shown that leverage increases the equity beta less rapidly under corporate taxes. This occurs because, under taxes, leverage creates a riskless tax shield, thereby lowering the risk of the entire firm.

EXAMPLE 17.3 Unlevered Betas Ross McDermott plc is considering a scale-enhancing project. The market value of the firm’s debt is £100 million, and the market value of the firm’s equity is £200 million. The debt is considered riskless. The corporate tax rate is 28 per cent. Regression analysis indicates that the beta of the firm’s equity is 2. The risk-free rate is 10 per cent, and the expected market premium is 8.5 per cent. What would the project’s discount rate be in the hypothetical case that Ross McDermott plc is all-equity? We can answer this question in two steps. Determining beta of hypothetical all-equity firm: Rearranging Eq. (17.4), we have this: Unlevered beta: Determining discount rate: We calculate the discount rate from the security market line (SML) as follows: Discount rate:

The Project Is not Scale Enhancing

p. 479Because the previous example assumed that the project is scale enhancing, we began with the beta of the firm’s equity. If the project is not scale enhancing, we could begin with the equity betas of firms in the industry of the project. For each firm, we could calculate the hypothetical beta of the unlevered equity by Eq. (17.5). The SML could then be used to determine the project’s discount rate from the average of these betas.

EXAMPLE 17.4

More Unlevered Betas

The Irish firm J. Lowes plc, which currently manufactures staples, is considering a €1 million investment in a project in the aircraft adhesives industry. The corporation estimates unlevered after-tax cash flows (UCF) of €300,000 per year into perpetuity from the project. The firm will finance the project with a debt-to-value ratio of 0.5 (or, equivalently, a debt-to-equity ratio of 1:1). The three competitors in this new industry are currently unlevered, with betas of 1.2, 1.3 and 1.4. Assuming a risk-free rate of 5 per cent, a market risk premium of 9 per cent, and a corporate tax rate of 12.5 per cent, what is the net present value of the project? We can answer this question in five steps. Calculating the average unlevered beta in the industry: The average unlevered beta across all three existing competitors in the aircraft adhesives industry is Calculating the levered beta for J. Lowes’s new project: Assuming the same unlevered beta for this new project as for the existing competitors, we have, from Eq. (17.4), Levered beta: Calculating the cost of levered equity for the new project: We calculate the discount rate from the security market line (SML) as follows: Discount rate: Calculating the WACC for the new project: The formula for determining the weighted average cost of capital, RWACC, is Determining the project’s value: Because the cash flows are perpetual, the NPV of the project is

Summary and Conclusions

p. 480Earlier chapters of this text showed how to calculate net present value for projects of all-equity firms. We pointed out in the last two chapters that the introduction of taxes and bankruptcy costs changes a firm’s financing decisions. Rational corporations should employ some debt in a world of this type. Because of the benefits and costs associated with debt, the capital budgeting decision for levered firms is different from that for unlevered firms. The present chapter has discussed three methods for capital budgeting by levered firms: the adjusted present value (APV), flows to equity (FTE), and weighted average cost of capital (WACC) approaches.

1. The APV formula can be written as
   
   There are four additional effects of debt:
   
   1. Tax shield from debt financing
   2. Flotation costs
   3. Bankruptcy costs
   4. Benefit of non-market-rate financing
2. The FTE formula can be written as
   
3. The WACC formula can be written as
   
4. Corporations frequently follow this guideline:
   
   1. Use WACC or FTE if the firm’s target debt-to-value ratio applies to the project over its life.
   2. Use APV if the project’s level of debt is known over the life of the project.
5. The APV method is used frequently for special situations such as interest subsidies, LBOs, and leases. The WACC and FTE methods are commonly used for more typical capital budgeting situations. The APV approach is a rather unimportant method for typical capital budgeting situations.
6. The beta of the equity of the firm is positively related to the leverage of the firm.